Introduction to Mathematical Philosophy is a work by Bertrand Russell, written in part to discuss less technically the central concepts of his and Whitehead's Principia Mathematica, including the theory of descriptions. Historically speaking, mathematics and logic have been entirely distinct studies. Mathematics connected with science and logic with Greek. But now, both have developed in contemporary times: philosophy has become more and more mathematical, and mathematics has become more logical. The obvious consequence is that it has now become completely impossible to draw a line to separate the two; in fact, now, both are one. They contrast as boy and man: logic is the youth version of mathematics and mathematics is the adulthood of logic. Logicians dislike this because, having spent their time in the study of classical texts, are incompetent to follow a piece of symbolic reasoning, and also by mathematicians who have learned a technique without bothering to inquire into its proof, meaning, or justification. Both types are fortunately growing rarer. So much that modern mathematical work is obviously on the borderline of logic, and modern philosophy is formal and symbolic, that the very close relationship between logic and mathematics are evident to every instructed student. The proof of it is a matter of detail. Beginning with premises that would be universally admitted to belong to logic, and arriving by deduction at results which as unmistakably belong to mathematics, we now find that there is no purpose for a sharp line to divide them, with logic and mathematics side by side. If there are still people who do not recognize the identity of logic and mathematics, we may challenge them to indicate the reason, in the successive definitions and conclusions of Principia Mathematica concludes that logic ends and math begins. It will then be evident that any answer need be entirely arbitrary.